VTMO 2015 — Grade 7 — final Question 4

If $\frac{a}{b} = \frac{c}{d}$, prove $\frac{a^{2} + b^{2}}{c^{2} + d^{2}} = \frac{ab}{cd}$ where defined. Also minimize $\frac{6}{| x | - 3}$ for integer $x$.